Method and apparatus for estimating the phase of a signal

ABSTRACT

An input signal is a complex vector whose phase is a coherent measurement of the phase rotation occurring between two separated symbols of a received CDMA signal. A processing block ( 30 ) provides a first signal showing the magnitude and the sign of the imaginary part of the input signal, and a second signal showing the magnitude and sign of the real part of the input signal to an initialisation block ( 31 ). A quadrant determination block ( 32 ) examines the signs of the signals to determine the quadrant in which the phase of the input signal exists. A comparator block ( 33 ) determines if the magnitude of the first signal is greater than or equal to the magnitude of the second signal. If a negative determination is made, the magnitude of the first signal is doubled in a multiplication block ( 35 ) to form a multiplied signal, and a counter incremented, initially from zero. The comparator block ( 33 ) then determines if the multiplied signal is greater than or equal to the magnitude of the second signal. This continues until the multiplied signal is equal to or exceeds the magnitude of the second signal. Carried to an upscaling block ( 36 ) is the multiplied signal (or the first signal if there is no multiplied signal), the magnitude of the second signal and the count of the counter (M). The upscaling block ( 36 ) examines the multiplied signal (or the first signal) and determines an upscaling factor. The multiplied signal (or the first signal) is multiplied by the scaling factor, as is the second signal, and the upscaled signals are provided to an angle determination block ( 34 ). The phase error θe in degrees is estimated by the formula θe=45°/2M.

[0001] This invention relates to a method for estimating the phase of asignal of interest, and to apparatus for estimating the phase of asignal of interest.

[0002] In accordance with a first aspect of this invention, there isprovided a method of estimating the phase rotation of a signal ofinterest from first and second signals, the method comprising:

[0003] a) determining whether a predetermined relationship existsbetween the magnitudes of the first and second signals;

[0004] b) if the predetermined relationship is determined to exist,moving to step g);

[0005] c) if the predetermined relationship does not exist, multiplyingthe first signal by a predetermined scaling factor to produce amultiplied signal;

[0006] d) determining whether the predetermined relationship existsbetween the multiplied signal and the second signal;

[0007] e) if the predetermined relationship does not exist between themultiplied signal and the second signal, multiplying the multipliedsignal by the predetermined scaling factor;

[0008] f) repeating steps d) and e) until the predetermined relationshipexists;

[0009] g) determining on how many occasions a signal was multipliedbefore the predetermined relationship came to exist; and

[0010] h) estimating the phase rotation using the number of occasions ofmultiplication so determined.

[0011] In accordance with a second aspect of this invention, there isprovided apparatus for estimating the phase rotation of a signal ofinterest from first and second signals, the apparatus comprising:

[0012] means for determining whether a predetermined relationship existsbetween the magnitudes of the first and second signals;

[0013] means for, if the predetermined relationship does not exist,multiplying the first signal by a predetermined scaling factor toproduce a multiplied signal;

[0014] means for determining whether the predetermined relationshipexists between the multiplied signal and the second signal;

[0015] means for, if the predetermined relationship does not existbetween the multiplied signal and the second signal, repeatedlymultiplying the multiplied signal by the predetermined scaling factoruntil the predetermined relationship exists;

[0016] means for determining on how many occasions a signal wasmultiplied before the predetermined relationship came to exist, andmeans responsive to the number of occasions of multiplication sodetermined for estimating the phase rotation.

[0017] This invention allows frequency error mitigation to beaccomplished without the extensive use of fixed point calculations andwithout using floating point calculations.

[0018] Embodiments of the present invention will now be described, byway of example only, with reference to the accompanying drawings, inwhich:

[0019]FIG. 1 shows schematically part of a finger of a rake receiver towhich the invention is applied;

[0020]FIG. 2 shows a flow diagram of a mathematical operation used todetermine a frequency error in accordance with the invention; and

[0021]FIG. 3 shows the phase error obtained using the FIG. 2mathematical operation.

[0022] A finger 10 of a rake receiver to which the invention is appliedis shown in FIG. 1. Referring to FIG. 1, the finger 10 comprisesgenerally a traffic channel 11 and a pilot channel 12. A mixer 13 in thetraffic channel 11 mixes an input signal, received from a schematicdelay line 14, with a code provided by a scrambling code generator 15and with a traffic channel specific code provided by a first OVSF codegenerator 16. The resultant signal is fed to a first accumulator 17 andto a first-in-first-out (FIFO) buffer 18, in a conventional manner. Inthe pilot channel 12, the input signal is mixed, in a second mixer 19,with the code provided by the scrambling code generator 15 and with apilot channel specific code, generated by a second OVSF code generator20. This mixed signal is then accumulated in a second accumulator 21over a period of time equal to 256 chips, or one symbol, of thescrambling code before being reset. The reset period of the secondaccumulator is aligned with reset period of the OVSF code provided bythe first OVSF code generator 16. The resultant complex signals are fedto a second delay line 22 and, from there, to a complex multiplier 23via a coherent phase reference device 24. The complex multiplier 23multiplies the output signals from the traffic channel 11 and the pilotchannel 12, the result being provided to a coherent combiner (not shown)along with signals from other fingers (not shown) of the rake receiver.

[0023] The code generators 15, 16 and 20 are symbol locked with eachother and run at code rate.

[0024] The complex value at a location P(n) in the second delay line 22is provided to a first input of a multiplier 25. The conjugate of acomplex value at another location P(n+k) in the second delay line 22 iscalculated by a conjugate calculation device 26, and the result provideda second input of the multiplier 25. The multiplier 25 multiplies thetwo complex numbers it receives, and provides the resulting complexnumber at an output 27. Initially, the value of k is set to 2, thelocation P(n) then corresponding to an accumulation result two symbolssubsequent to the location P(n+2). The second delay line 22 operates ina rolling manner such that, when another accumulation result is providedby the second accumulator 21, this is fed through the second delay lineand the multiplier 25 is then fed with signals from subsequent locationsin the second delay line. A new complex number output is, therefore,provided every symbol.

[0025] The complex number output is a complex vector whose phase is acoherent measurement of the phase rotation occurring between the symbolscorresponding to the locations P(n) and P(n+k). The magnitude of thecomplex vector is proportional to the average power of the accumulationresults from those two symbols.

[0026] Referring now to FIG. 2, the complex number provided by themultiplier is received at a processing block 30, which provides a firstsignal which is a 32 bit binary number showing the magnitude and thesign of the imaginary part of the output signal of the multiplier 25,and a second signal which is a 32 bit binary number showing themagnitude and sign of the real part of the output signal of themultiplier. These first and second signals are passed to aninitialisation block 31, from where they are passed both to a quadrantdetermination block 32 and to a comparator block 33. The quadrantdetermination block 32 examines the signs of the first and secondsignals to determine the quadrant in which the phase of the input signalexists, and provides the result to an angle determination block 34.

[0027] The comparator block 33 determines if the magnitude of the firstsignal is greater than or equal to the magnitude of the second signal.If a negative determination is made, the magnitude of the first signalis doubled in a multiplication block 35 to form a multiplied signal, anda counter incremented from zero to one. Doubling is effected by a singleleftwards bit shift of the first signal and by filling the lastsignificant bit with a ‘zero’. The comparator block 33 then determinesif the multiplied signal is greater than or equal to the magnitude ofthe second signal. If a negative determination is again made, themultiplied signal is doubled in the multiplication block to provide arevised multiplied signal, and the counter is again incremented. Thisprocess continues until the multiplied signal is equal to or exceeds themagnitude of the second signal, when progression is made to an upscalingblock 36. The information carried to the upscaling block 36 is themultiplied signal (or the first signal if there is no multipliedsignal), the magnitude of the second signal and the count of thecounter. The count of the counter can be considered to be amultiplication factor. If the magnitude of the first signal was equal toor greater than the magnitude of the second signal i.e. no multipliedsignals were calculated, the multiplication factor is zero.

[0028] The upscaling block 36 examines the multiplied signal or thefirst signal, as the case may be, and determines how much the signal canbe upscaled before it would exceed the limit imposed by the 32 bitsassigned to accommodate the signals. The degree of upscaling sodetermined is hereafter termed the upscaling factor. The multipliedsignal or the first signal, as the case may be, is multiplied by thescaling factor, as is the second signal, and the upscaled signals areprovided to the angle determination block 34.

[0029] The phase error θ_(e) in degrees, is then estimated by thefollowing formula:

θ_(e)=45°/2^(M)

[0030] where M is the count of the counter.

[0031]FIG. 3 shows how this estimated phase error differs from theactual phase error. Referring to FIG. 3, the tan of the phase 40, whichis indicative of the true phase error, is shown next to a linearapproximation 41 thereof. The quantisation levels 42-44 result from thedoubling and comparing effected by the multiplication block 35 and thecomparing block 33. The difference between the phase error obtainedusing the above formula and the actual phase error is shown at 45-47.

[0032] Referring again to FIG. 2, the calculated phase error is fed toan angle-to-frequency error conversion block 37, where a (possiblyupscaled) frequency error f_(e) is calculated using the followingformula:${fe} = \frac{\theta \quad e}{2{\pi \left( {{Tm}/C} \right)}}$

[0033] Where θ_(e) is the calculated phase error, T_(m) is themeasurement period in chips (initially 512 chips), and C is the chiprate. The frequency error f_(e) is rounded down to the nearest integer.

[0034] This frequency error f_(e) is then downscaled by dividing it bythe upscaling factor in a downscaling block 38, and the resultingfrequency error provided at an output. The frequency error is fed backto control the frequency of an oscillator (not shown) forming part ofthe rake receiver. The upscaling and subsequent downscaling results inimproved accuracy of frequency error estimation since it reducesquantisation noise.

[0035] The downscaling block 38 is arranged such that it does notprovide a frequency error signal which corresponds to a phase error inthe region of −1° to +1°. If such a frequency error would be provided,the frequency error signal is increased incrementally until thiscriteria is met. Accordingly, once approximate convergence of thefrequency of the received signals with the downconversion frequencyeffected in the rake receiver is reached, the error swings from one sideof the true frequency to the other side, and so on.

[0036] Once convergence is reached, the value of k is increased, so thatthe multiplier 25 receives signals which correspond to accumulationresults spaced further apart in time. This allows more accurate phase,and therefore frequency, error signals to be calculated.

[0037] This invention allows a phase error, and therefore a frequencyerror, signal to be provided with relatively few fixed-point operationsand with no floating-point operations. The apparatus required is,therefore, of simpler construction than conventional digital phase andfrequency error estimation apparatus. The resultant frequency errorsignals are not, however, as accurate as those obtained conventionally,but the inventors see this as a disadvantage which is acceptable in viewof the advantages obtained. The invention can be used both withacquisition and with tracking of the carrier of received signals, and isnot limited to use with code division multiple access receivers.

[0038] Although the invention has been described with the multiplicationblock providing a doubling function, other scaling factors are possible,such as four and eight, although larger scaling factors result indecreased accuracy.

1. A method of estimating the phase rotation of a signal of interestfrom first and second signals, the method comprising: a) determiningwhether a predetermined relationship exists between the magnitudes ofthe first and second signals; b) if the predetermined relationship isdetermined to exist, moving to step g); c) if the predeterminedrelationship does not exist, multiplying the first signal by apredetermined scaling factor to produce a multiplied signal; d)determining whether the predetermined relationship exists between themultiplied signal and the second signal; e) if the predeterminedrelationship does rot exist between the multiplied signal and the secondsignal, multiplying the multiplied signal by the predetermined scalingfactor; f) repeating steps d) and e) until the predeterminedrelationship exists; g) determining on how many occasions a signal wasmultiplied before the predetermined relationship came to exist; and h)estimating the phase using the number of occasions of multiplication sodetermined.
 2. A method according to claim 1, wherein the predeterminedrelationship exists when the magnitude of the first signal is greaterthan, or is greater than or equal to, the magnitude of the secondsignal.
 3. A method according to any preceding claim, wherein the firstand second signals are provided by: mixing a signal having a known datasequence with a de-spreading code; accumulating the mixed signal over afirst period of time to provide a first complex value; accumulating themixed signal over a second period of time, separated from the firstperiod of time, to provide a second complex value; multiplying the firstcomplex value by the conjugate of the second complex value; taking thereal part of the multiplication result as the second signal; and takingthe imaginary part of the multiplication result as the first signal. 5.A method according to any preceding claim, further comprisingdetermining the quadrant of the phase of the signal of interest byexamining the signs of the first and second signals.
 6. A methodaccording to any preceding claim, further comprising adjusting theseparation of the first and second periods of time.
 7. A methodaccording to any preceding claim, further comprising upscaling thesecond signal, and upscaling the first signal or, if the first signalwas multiplied before the predetermined relationship existed, upscalingthe multiplied signal which resulted in the predetermined relationshipexisting.
 8. Apparatus for estimating the phase rotation of a signal ofinterest from first and second signals, the apparatus comprising: meansfor determining whether a predetermined relationship exists between themagnitudes of the first and second signals; means for, if thepredetermined relationship does not exist, multiplying the first signalby a predetermined scaling factor to produce a multiplied signal; meansfor determining whether the predetermined relationship exists betweenthe multiplied signal and the second signal; means for, if thepredetermined relationship does not exist between the multiplied signaland the second signal, repeatedly multiplying the multiplied signal bythe predetermined scaling factor until the predetermined relationshipexists; means for determining on how many occasions a signal wasmultiplied before the predetermined relationship came to exist; andmeans responsive to the number of occasions of multiplication sodetermined for estimating the phase rotation.
 9. Apparatus according toclaim 8, wherein the means for determining whether predeterminedrelationship exists comprises means for detecting when the magnitude ofthe first signal is greater than, or is greater than or equal to, themagnitude of the second signal.
 10. Apparatus according to claim 8 orclaim 9, further comprising means to provide the first and secondsignals, the means comprising: a mixer for mixing a signal having aknown data sequence with a de-spreading code; an accumulator foraccumulating the mixed signal over a first period of time to provide afirst complex value and for accumulating the mixed signal over a secondperiod of time, separated from the first period of time, to provide asecond complex value; means for multiplying the first complex value bythe conjugate of the second complex value; means for taking the realpart of the multiplication result as the second signal; and means fortaking the imaginary part of the multiplication result as the firstsignal.
 11. Apparatus according to any of claims 8 to 10, furthercomprising means for examining the signs of the first and second signalsto determine the quadrant of the phase of the signal of interest. 12.Apparatus according to any of claims 8 to 11, further comprising meansfor adjusting the separation of the first and second periods of time.13. Apparatus according to any of claims 8 to 12 further comprisingmeans for upscaling the second signal, and means for upscaling the firstsignal or, if it is determined that the first signal was multipliedbefore the predetermined relationship existed, upscaling the multipliedsignal which resulted in the predetermined relationship existing.